On 10/30/09 at 2:19 AM, lawrenceteo at yahoo.com (Lawrence Teo) wrote:
>We know that Simplify[Cos[x]^2-Sin[x]^2] -> Cos[2 x] But why
>Simplify[Cos[x]^4-Sin[x]^4] -> Cos[2 x] too?
>Doing subtraction between the two expressions will give small delta.
>This is enough to prove that the two expression shouldn't be the
>same.
When you did the subtraction did you do:
In[5]:= Cos[x]^2 - Sin[x]^2 - (Cos[x]^4 - Sin[x]^4) // Simplify
Out[5]= 0
which is correct. Or did you fail to include the parentheses and do
In[6]:= Cos[x]^2 - Sin[x]^2 - Cos[x]^4 - Sin[x]^4 // Simplify
Out[6]= -2 sin^4(x)
Since, this result could be characterized as a "small delta", my
guess is this is what you did. But this is not the difference
between the two expressions.